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\date{}

\begin{document}

\hypertarget{header-n0}{%
\section{DMAA Homework \#03}\label{header-n0}}

\hypertarget{header-n3}{%
\subsection{5.1. Following the training data set the table 5.1, use
algorithm C4.5 to build a decision tree.}\label{header-n3}}

Solution:

Solution:\\
The solution method is

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\item
  Compute \(H(D)\).
\item
  Compute \(H(D|A_{i}) , \quad i=1,2,3,4\).
\item
  Compute \(H_{A_{i}}(D),  \quad (i=1,2,3,4)\).
\item
  Compute \(g_{R}(D,A_{i}), \quad (i=1,2,3,4)\).
\item
  Following algorithm C4.5...
\end{enumerate}

In fact the computation process is tooooooo long and tooooooo dull, I
just put few computation process like below.

\[H(D)=- \frac{6}{15} \log_{2}\frac{6}{15} - \frac{9}{15}\log_{2}\frac{9}{15}=0.97095,
\\
g_{R}(D,A_{1}) = 0.05237, \quad g_{R}(D,A_{2}) = 0.35244, \quad g_{R}(D,A_{1}) = 0.43253,\quad g_{R}(D,A_{1}) =0.23179\]

\begin{figure}
\hypertarget{mermaid}{%
\centering
\includegraphics[width=2.05208in,height=\textheight]{1616936165062.png}
\caption{}\label{mermaid}
}
\end{figure}

\hypertarget{header-n63}{%
\subsection{5.2. Known as the training data set from table 5.2, try to
build a binary regression tree with loss of square error
criterion.}\label{header-n63}}

Solution:

\begin{figure}
\centering
\includegraphics{/home/zjulhl18/.config/Typora/typora-user-images/image-20210328054735821.png}
\caption{}
\end{figure}

\hypertarget{header-n68}{%
\subsection{\texorpdfstring{5.3. Proof: in the CART pruning algorithm,
with certain a, there exists unique min child-tree \(T_{\alpha}\) that
make the loss function \(C_{\alpha}\)
min.}{5.3. Proof: in the CART pruning algorithm, with certain a, there exists unique min child-tree T\_\{\textbackslash{}alpha\} that make the loss function C\_\{\textbackslash{}alpha\} min.}}\label{header-n68}}

Solution:

If there have more than two "min-child-tree", we can find a pruning node
from one of the trees in other trees to make the loss less, so there can
be more than two "min-child-tree".

\end{document}
